Welcome to the Matrix Operations Tutorial! In this guide, we will explore the fundamental operations performed on matrices, including addition, subtraction, multiplication, and more. Matrices are a cornerstone of linear algebra and have applications in various fields such as physics, engineering, and computer science.

Basic Matrix Operations

Matrix Addition

Matrix addition involves adding the corresponding elements of two matrices. The resulting matrix will have the same dimensions as the original matrices.

  • Example: 
    Matrix A:
| 1 2 |
| 3 4 |

Matrix B:
| 5 6 |
| 7 8 |
    Sum:
    | 1+5 2+6 |
| 3+7 4+8 |
    Result:
    | 6 8 |
| 10 12 |

Matrix Subtraction

Matrix subtraction is similar to matrix addition, but instead of adding the corresponding elements, we subtract them.

  • Example: 
    Matrix A:
| 1 2 |
| 3 4 |

Matrix B:
| 5 6 |
| 7 8 |
    Difference:
    | 1-5 2-6 |
| 3-7 4-8 |
    Result:
    | -4 -4 |
| -4 -4 |

Matrix Multiplication

Matrix multiplication involves multiplying the rows of the first matrix by the columns of the second matrix. The resulting matrix will have a new dimension of rows from the first matrix and columns from the second matrix.

  • Example: 
    Matrix A:
| 1 2 |
| 3 4 |

Matrix B:
| 5 6 |
| 7 8 |
    Product:
    | 1*5 + 2*7 1*6 + 2*8 |
| 3*5 + 4*7 3*6 + 4*8 |
    Result:
    | 19 22 |
| 43 50 |

For more information on matrix operations and their applications, check out our Matrix Theory guide.

Matrix